Using first-principles molecular dynamics, we calculated the equation of state and shock Hugoniot of various boron phases. We find a large mismatch between Hugoniots based on existing knowledge of the equilibrium phase diagram and those measured by shock experiments, which could be reconciled if the $α$-B$_{12}$/$β\rightarrowγ$-B$_{28}$ transition is significantly over-pressurized in boron under shock compression. Our results also indicate that there exists an anomaly and negative Clapeyron slope along the melting curve of boron at 100 GPa and 1500--3000 Kelvin. These results enable in-depth understanding of matter under shock compression, in particular the significance of compression-rate dependence of phase transitions and kinetic effects in experimental measurements.
We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1$\times$10$^4$-5.2$\times$10$^8$ K) and densities (0.25-49 g/cm$^3$), and experimental shock Hugoniot data at unprecedented high pressures (5608$\pm$118 GPa). The calculations are performed with full, first-principles methods combining path integral Monte Carlo (PIMC) at high temperatures and density functional theory molecular dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference $<$1.5 Hartree/boron in energy and $<…
Boron carbide is a ceramic material with unique properties widely used in numerous, including armor, applications. Its mechanical properties, mechanism of compression, and limits of stability are of both scientific and practical value. Here, we report the behavior of the stoichiometric boron carbide B13C2 studied on single crystals up to 68 GPa. As revealed by synchrotron X-ray diffraction, B13C2 maintains its crystal structure and does not undergo phase transitions. Accurate measurements of the unit cell and B12 icosahedra volumes as a function of pressure led to conclusion that they reduce s…
Density Functional Theory calculations using the quasi-harmonic approximation have been used to calculate the solid Hugoniot of two polytypes of boron carbide up to 100 GPa. Under the assumption that segregation into the elemental phases occurs around the pressure that the B11Cp(CBC) polytype becomes thermodynamically unstable with respect to boron and carbon, two discontinuities in the Hugoniot, one at 50 GPa and one at 90-100 GPa, are predicted. The former is a result of phase segregation, and the latter a phase transition within boron. First principles molecular dynamics (FPMD) simulations …
Quantum molecular dynamic simulations are introduced to study the dynamical, electrical, and optical properties of carbon dioxide under dynamic compressions. The principal Hugoniot derived from the calculated equation of states is demonstrated to be well accordant with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions, and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are a…
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculat…
We report results of molecular dynamics simulation of shock wave propagation in silicon in [100], [110], and [111] directions obtained using a classical environment-dependent interatomic potential (EDIP). Several regimes of materials response are classified as a function of shock wave intensity using the calculated shock Hugoniot. Shock wave structure in [100] and [111] directions exhibit usual evolution as a function of piston velocity. At piston velocities km/s the shock wave consists of a fast elastic precursor followed by a slower plastic front. At larger piston velocities the single overd…
Based on his 50-year career in static high-pressure research, P. W. Bridgman (PWB) is the father of modern high-pressure physics. What is not generally recognized is that Bridgman was also intimately connected with establishing shock compression as a scientific tool and he predicted major events in shock research that occurred up to 40 years after his death. In 1956 the first phase transition under shock compression was reported in Fe at 13 GPa (130 kbar). PWB said a phase transition could not occur in a ~microsec, thus setting off a controversy. The scientific legitimacy of shock compression …
The high-pressure melting curve of tantalum (Ta) has been the center of a long-standing controversy. Sound velocities along the Hugoniot curve are expected to help in understanding this issue. To that end, we employed a direct-reverse impact technique and velocity interferometry to determine sound velocities of Ta under shock compression in the 10-110 GPa pressure range. The measured longitudinal sound velocities show an obvious kink at ~60 GPa as a function of shock pressure, while the bulk sound velocities show no discontinuity. Such observation could result from a structural transformation …
We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. E…
Silicon (Si) is one of the most abundant elements on Earth, and it is the most important and widely used semiconductor, constituting the basis of modern electronic devices. Despite extensive study, some properties of Si remain elusive. For example, the behaviour of Si under high pressure, in particular at the ultra-high strain rates characteristic of dynamic compression, has been a matter of debate for decades. A detailed understanding of how Si deforms is crucial for a variety of fields, ranging from planetary science to materials design. Simulations suggest that in Si the shear stress genera…
Due to its far-reaching applications in geophysics and materials science, quartz has been one of the most extensively examined materials under dynamic compression. Despite 50 years of active research, questions remain concerning the structure and transformation of SiO2 under shock compression. Continuum gas-gun studies have established that under shock loading quartz transforms through an assumed mixed-phase region to a dense high-pressure phase. While it has been often assumed that this high-pressure phase corresponds to the stishovite structure observed in static experiments, there has been …
The principal Hugoniot for liquid hydrogen was obtained up to 55 GPa under laser-driven shock loading. Pressure and density of compressed hydrogen were determined by impedance-matching to a quartz standard. The shock temperature was independently measured from the brightness of the shock front. Hugoniot data of hydrogen provide a good benchmark to modern theories of condensed matter. The initial number density of liquid hydrogen is lower than that for liquid deuterium, and this results in shock compressed hydrogen having a higher compression and higher temperature than deuterium at the same sh…
We employ quantum molecular dynamic simulations to investigate the behavior of benzene under shock conditions. The principal Hugoniot derived from the equation of state is determined. We compare our firs-principles results with available experimental data and provide predictions of chemical reactions for shocked benzene. The decomposition of benzene is found under the pressure of 11 GPa. The nonmetal-metal transition, which is associated with the rapid C-H bond breaking and the formation of atomic and molecular hydrogen, occurs under the pressure around 50 GPa. Additionally, optical properties…
Theoretical predictions of pressure-induced phase transformations often become long-standing enigmas because of limitations of contemporary available experimental possibilities. Hitherto the existence of a non-icosahedral boron allotrope has been one of them. Here we report on the first non-icosahedral boron allotrope, which we denoted as ζ-B, with the orthorhombic α-Ga-type structure (space group Cmce) synthesized in a diamond anvil cell at extreme high-pressure high-temperature conditions (115 GPa and 2100 K). The structure of ζ-B was solved using single-crystal synchrotron X-ray diffraction…
Quasi-hydrostatic compression of rhombohedral boron monosulfide (r-BS) has been studied up to 50 GPa at room temperature using diamond-anvil cells and angle-dispersive synchrotron X-ray diffraction. A fit of the experimental P-V data to the Vinet equation of state yields bulk modulus of 42.2(1.4) GPa and its first pressure derivative of 7.6(2) that are in excellent agreement with our ab initio calculations. Formation of a new high-pressure phase of boron monosulfide (hp-BS) has been observed above 35 GPa. According to ab initio evolutionary crystal structure predictions combined with Rietveld …
When a metallic specimen is plastically deformed, its underlying crystal structure must often rotate in order to comply with its macroscopic boundary conditions. There is growing interest within the dynamic compression community in exploiting x-ray diffraction measurements of lattice rotation to infer which combinations of plasticity mechanisms are operative in uniaxially shock- or ramp-compressed crystals, thus informing materials science at the greatest extremes of pressure and strain rate. However, it is not widely appreciated that several of the existing models linking rotation to slip act…
Quantum molecular dynamic simulations have been employed to study the equation of state (EOS) of fluid helium under shock compressions. The principal Hugoniot is determined from EOS, where corrections from atomic ionization are added onto the calculated data. Our simulation results indicate that principal Hugoniot shows good agreement with gas gun and laser driven experiments, and maximum compression ratio of 5.16 is reached at 106 GPa.
Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 $μ$m/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved…
Quantum molecular dynamic (QMD) simulations are introduced to study the thermophysical properties of liquid deuterium under shock compression. The principal Hugoniot is determined from the equation of states, where contributions from molecular dissociation and atomic ionization are also added onto the QMD data. At pressures below 100 GPa, our results show that the local maximum compression ratio of 4.5 can be achieved at 40 GPa, which is in good agreement with magnetically driven flyer and convergent-explosive experiments; At the pressure between 100 and 300 GPa, the compression ratio reaches …
The high-pressure phase stability of the metastable tetragonal zirconia is still under debate. The transition dynamics of shocked Y2O3 (3 mol%) stabilized tetragonal zirconia ceramics under laser-shock compression has been directly studied using nanosecond time-resolved X-ray diffraction. The martensitic phase transformation to the monoclinic phase, which is the stable phase for pure zirconia at ambient pressure and room temperature, has been observed during compression at 5 GPa within 20 ns without any intermediates. This monoclinic phase reverts back to the tetragonal phase during pressure r…
With the aid of nanosecond time-resolved X-ray diffraction techniques, we have explored the complex structural dynamics of bismuth under laser-driven compression. The results demonstrate that shocked bismuth undergoes a series of structural transformations involving four solid structures: the Bi-I, Bi-II, Bi-III and Bi-V phases. The transformation from the Bi-I phase to the Bi-V phase occurs within 4 ns under shock compression at ~11 GPa, showing no transient phases with the available experimental conditions. Successive phase transitions (Bi-V->Bi-III->Bi-II->Bi-I) during the shock release wit…
We use dedicated microfluidic devices to expose soft hydrogel particles to a rapid change in the externally applied osmotic pressure and observe a non-monotonic response: After an initial rapid compression the particle slowly reswells to approximately its original size. Using a simple phenomenological and a more elaborate poroelastic model, we extract important material properties from a single microfluidic experiment, including the compressive modulus, the gel permeability and the diffusivity of the osmolyte inside the gel. We expect our approach to be relevant to applications such as control…
Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Muséum National d’Histoire Naturelle（矿物学、材料物理与宇宙化学研究所，索邦大学，国家自然历史博物馆）；ISTerre, Université Grenoble Alpes（ISTerre实验室，格勒诺布尔阿尔卑斯大学）；Laboratoire pour l’Utilisation des Lasers Intenses (LULI), Ecole Polytechnique（高强度激光利用实验室（LULI），巴黎综合理工学院）；Earth and Planetary Sciences, Stanford University（地球与行星科学系，斯坦福大学）；School of Earth and Space Exploration, Arizona State University（地球与空间探索学院，亚利桑那州立大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）
High pressure and high temperature properties of AB (A = $^6$Li, $^7$Li; B = H, D, T) are investigated with first-principles method comprehensively. It is found that the H$^{-}$ sublattice features in the low-pressure electronic structure near the Fermi level of LiH are shifted to that dominated by the Li$^{+}$ sublattice in compression. The lattice dynamics is studied in quasi-harmonic approximation, from which the phonon contribution to the free energy and the isotopic effects are accurately modelled with the aid of a parameterized double-Debye model. The obtained equation of state (EOS) mat…
Wehrenberg et. al. [Nature 550 496 (2017)] used ultrafast in situ x-ray diffraction at the LCLS x-ray free-electron laser facility to measure large lattice rotations resulting from slip and deformation twinning in shock-compressed laser-driven [110] fibre textured tantalum polycrystal. We employ a crystal plasticity finite element method model, with slip kinetics based closely on the isotropic dislocation-based Livermore Multiscale Model [Barton et. al., J. Appl. Phys. 109 (2011)], to analyse this experiment. We elucidate the link between the degree of lattice rotation and the kinetics of plas…
A detailed understanding of the material response to rapid compression is challenging and demanding. For instance, the element gold under dynamic compression exhibits complex phase transformations where there exist some large discrepancies between experimental and theoretical studies. Here, we combined large-scale molecular dynamics simulations with a deep potential to elucidate the dynamic compression processes of gold from an atomic level. The potential is constructed by accurately reproducing the free energy surfaces of density-functional-theory calculations for gold, from ambient condition…
Solid usually becomes harder and tougher under compression, and turns softer at elevated temperature. Recently, compression-induced softening and heating-induced hardening (CISHIH) dual anomaly was predicted in group VB elements such as vanadium. Here, the evidence for this counterintuitive phenomenon is reported. By using accurate high-temperature high-pressure sound velocities measured at Hugoniot states generated by shock-waves, together with first-principles calculations, we observe not only the prominent compression-induced sound velocity reduction, but also strong heating-induced sound v…
The properties of hot dense helium at megabar pressures were studied with two first-principles computer simulation techniques, path integral Monte Carlo and density functional molecular dynamics. The simulations predicted that the compressibility of helium is substantially increased by electronic excitations that are present in the hot fluid at thermodynamic equilibrium. A maximum compression ratio of 5.24(4)-fold the initial density was predicted for 360 GPa and 150000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3(1). Hu…
Recently, deuterium has been the focus of a high level of experimental and theoretical activity that was sparked by a disagreement on the experimental value of the maximum compression along the Hugoniot. The behavior of deuterium at Mbar pressures is not well understood. It is of great interest to understand how the current uncertainty on the hydrogen/deuterium EOS affects the inferred structures of Jupiter and Saturn. In particular, the mass of a core of heavy elements (other than H and He) and the total mass of those heavy elements in these two planets are quite sensitive to the EOS of hydro…
Shock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining th…
We explore the response of the insensitive high explosive (IHE) 1,3,5-Triamino-2,4,6- trinitrobenzene (TATB) under detonation-induced shock conditions using in-situ synchrotron X-ray diffraction in the 100 ns time scale using either a conventional or a colliding detonation drive. In all of the detonation experiments on various sizes and morphologies of TATB, we observe an extended stability of the TATB triclinic crystal structure. As the detonation front passes through the TATB, X-ray diffraction indicates a portion of the TATB exhibits a compression up to 30+ GPa, followed subsequently by a p…
Compression wave analysis started nearly 50 years ago with Fowles.[1] Coperthwaite and Williams [2] gave a method that helps identify simple and steady waves. We have been developing a method that gives describes the non-isentropic character of compression waves, in general.[3] One result of that work is a simple analysis tool. Our method helps clearly identify when a compression wave is a simple wave, a steady wave (shock), and when the compression wave is in transition. This affects the analysis of compression wave experiments and the resulting extraction of the high-pressure equation of sta…
Using two first-principles computer simulation techniques, path integral Monte-Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11~g/cm$^3$~and temperatures from 20,000 K to $5\times10^8$~K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. We study ionization mechanisms and electronic structure of magnesium as a function of density and temperature. We sh…
The objective of this work is to define the parameters of the three-term equation of state for uranium and plutonium, appropriate for conditions in which these materials are subjected to strong shock compressions, as in cylindrical and spherical implosions. The three-term equation of state takes into account the three components of the pressure that resist to compression in the solid: the elastic or "cold" pressure (coulombian repulsion between atoms), the thermal pressure due to vibratory motion of atoms in the lattice of the solid and the thermal pressure of electrons thermally excited. The …
